Manifold based analysis of diffusion tensor images using isomaps

This paper addresses the problem of statistical analysis of diffusion tensor magnetic resonance images (DT-MRI)., DT-MRI cannot be analyzed by commonly used linear methods, due to the inherent non-linearity of tensors, which are restricted to lie on a non-linear sub-manifold of the space in which they are defined, namely IR ⁶. We perform statistical analysis on tensors by identifying the underlying manifold of the set of tensors under consideration using the Isomap manifold learning technique. Multivariate statistics are then performed on this estimated manifold using geodesic distances between tensors, thereby warranting that the analysis is restricted to the proper subspace of R ⁶. Experimental results on data with known ground truth show that the proposed statistical analysis method properly captures statistical relationships among tensor image data, and it identifies group differences. Comparisons, with standard statistical analyses that rely on Euclidean, rather than geodesic distances, are also discussed.